Introduction To Partial Differential Equations

Introduction To Partial Differential Equations Book Description

The goal of this book is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read more advanced treatises. The author assumes no previous knowledge of partial differential equations (though first courses in real analysis and complex analysis are the prerequisites).

Much of the theory of partial differential equations as it now stands has its roots in the study of second-order operators from mathematical physics-the Laplace, heat and wave operators. After dealing with the classical theory, first-order equations, and local existence theorems in the first two chapters, the book concentrates on a detailed discussion of these operators in the next three chapters. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics.

The theory of pseudodifferential operators has become one of the most essential tools in the modern theory of differential equations, as it offers a powerful and flexible way of applying Fourier techniques to the study of variable-coefficient operators and singularities of distributions. The last three chapters cover the modern theory-Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.

The book includes quite a few exercises in each chapter to enhance student learning.

This well-written, accessible introduction to partial differential equations is suitable as a text for mathematics students at the postgraduate level.

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